sql-machine-learning-services setup: RegisterRext.exe aborts with “MPI installation was not found”

In  a SQL Server 2022 environment I  have a problem in setting up the sql-machine-learning-services. When Configure Python runtime with SQL Server, executing the RegisterRext.exe command results in an error message “MPI installation was not found”

I have been following the steps at this site

 https://learn.microsoft.com/en-us/sql/machine-learning/install/sql-machine-learning-services-windows-install-sql-2022?view=sql-server-ver16

In The Python section, an error occures when executing

.\RegisterRext.exe /configure /pythonhome:"C:\Program Files\Python312" /instance:"MSSQLSERVER"

Error:

….

Granting NT Service\MSSQLLaunchpad ReadAndExecute permission to C:\Program Files\Python312 ...

Granted NT Service\MSSQLLaunchpad ReadAndExecute permission to C:\Program Files\Python312

Error: Exception occurred in Settings Install

Failed to complete the operation successfully.

Usage

….

The logfile RegisterRExt.log shows the detailed error:

 Granted NT Service\MSSQLLaunchpad ReadAndExecute permission to C:\Program Files\Python312

 --   DateTime=2024-01-07T08:41:21.2670000Z

 --Error: 0 : System.Exception: Exception occurred in Settings Install ---> System.IO.DirectoryNotFoundException: MPI installation was not found.

 --  bei Microsoft.SqlServer.Server.Settings.GetFirstValidPath(IEnumerable`1 paths, String exceptionString)

 --  bei Microsoft.SqlServer.Server.Settings..ctor(ParsedArguments parsedArgs, String instancePath, Boolean isXcopyInstall, Boolean isAppContainerEnabled, String sqlExtDataPath)

 --  bei Microsoft.SqlServer.Server.Settings.Install(ParsedArguments parsedArgs, String binnPath, Boolean isXcopyInstall, FileSecurity fileSecurity)

 --  --- Ende der internen Ausnahmestapelüberwachung ---

 --  bei Microsoft.SqlServer.Server.Settings.Install(ParsedArguments parsedArgs, String binnPath, Boolean isXcopyInstall, FileSecurity fileSecurity)

 --  bei Microsoft.SqlServer.Server.Program.Main(String[] args)

 --   DateTime=2024-01-07T08:41:21.2826203Z

 --Information: 0 : Failed to complete the operation successfully.

Environment is

Microsoft SQL Server Express (64-bit) ( SQL Server 2022 (RTM-GDR) (KB5032968) - 16.0.1110.1 (X64))

,Windows 10 , Version 22H2

Python 3.12.1

After installing and setup MPI the error remained the same. I need help regarding this problem.